Architectural system using a retractable strut aligned in a base plane and an extension strut protruding acutely from the base plane

ABSTRACT

In an architectural system, a triangular base engages an extension. The base includes three complete struts substantially aligned along their respective axes. These axes each intersect each other to form a triangle contained in a base plane. The triangle&#39;s vertices each correspond to a respective nucleus of nodes called A, B and C. This forms three base angles. The first angle has a positive value about equal to [j×20.9°+k×31.7°+m×36°+n×37.4°], where j, k, m and n are each an integer less than three. The second angle also has a positive value about equal to [q×20.9°+r×31.7°+s×36°+t×37.4°], where q, r, s and t are each an integer less than three. The third node engages the second and third complete struts and must be large enough to maintain the third base angle at a positive value less than 60°. 
     At least one of the base triangle struts comprises two or more rigid pieces able to move apart so as to produce a strut elongation. The extension comprises a fourth complete strut substantially aligned along a fourth axis forming a substantially acute angle &gt;3° with the base plane.

FIELD OF THE INVENTION

This application relates generally to architectural systems and more particularly to node and strut configurations.

BACKGROUND OF THE INVENTION

Despite the many advances in materials over the past several decades, and the continuing interest in alternative building styles such as dome structures, the use of spaceframes in construction continues to be rather limited. Although node and strut systems have been devised and used by some, only very limited types of geometries, generally those based on the cube or pyramid, have achieved widespread use.

One noteworthy exception is the pioneering work of Steve Baer, who on 27 Mar. 1973 was issued U.S. Pat. No. 3,722,153 (“Structural System”). The Baer patent teaches rigid, lightweight systems of nodes and struts, but does not provide any mechanism for ensuring rigid engagement between nodes and struts in a complex spaceframe. The teaching in the Baer patent is likewise limited by the small number of varieties of base triangles included.

Further, useful advances were taught in U.S. Pat. No. 5,265,395 (“Node Shapes of Prismatic Symmetry for a Spaceframe Building System”) issued 30 Nov. 1993 to Haresh Lalvani. The Lalvani patent teaches nodes and struts of various geometries, but does not teach any system for using struts to rigidly couple adjacent layers. A similar design, simpler than Lalvani's but also lacking inter-layer triangulation, is shown in FIG. 5 below.

Those skilled in the art have overlooked substantial benefits that might be achieved in economies of mass production, versatility, high rigidity, low weight and/or ease of assembly in architectural systems incorporating golden geometry. It is to these opportunities that the present invention is directed.

SUMMARY OF THE INVENTION

The present invention is an architectural system that, in its most basic form, includes a triangular base which engages an extension. The base includes three “complete” struts (defined in the detailed description below) substantially aligned along three respective axes. These axes each intersect each other to form a triangle defining in a base plane. The triangle's vertices each correspond to a respective nucleus (described below) of nodes called A, B and C. This forms three base angles (called CAB, ABC, and CBA). Angle CAB has a positive value about equal to [j×20.9°+k×31.7°+m×36°+n×37.4°], where j, k, m and n are each an integer less than three. Angle ABC also has a positive value about equal to [q×20.9°+r×31.7°+s×36°+t×37.4°], where q, r, s and t are each an integer less than three. Subject to certain geometric restraints such as the necessity for the interior angles of a triangle to total 180°, these eight coefficient values can vary somewhat independently.

At least one of the base triangle struts comprises at least two rigid pieces able to move apart so as to produce a strut elongation. In a complex spaceframe where each node has a position constrained by struts already engaging it, each new strut installed should desirably have such a length correction mechanism so as to permit positive (areal) engagement with its nodes.

The extension comprises (at least) a fourth complete strut substantially aligned along a fourth axis that is neither coplanar with nor orthogonal to the base plane. The fourth axis, in fact, forms a substantially acute angle >3° with the base plane. (Although additional extension struts may be orthogonal, adequate structural triangulation might not be achieved without at least one such acute angle.)

These and various other features as well as additional advantages which characterize the present invention will be apparent from a reading of the following detailed description and a review of the associated drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a basic architectural system of the present invention comprising a triangular base and an extension protruding therefrom.

FIG. 2 is a chart summarizing which figures in this description illustrate which integer values as used in the formulas described in the summary.

FIG. 3 shows a simple, trilaterally symmetric architectural system of the present invention, suitable for use in a table.

FIG. 4 shows an enlarged view of the respective positions of the nuclei of some of the nodes of FIG. 3.

FIG. 5 shows a simple but sub-optimal architectural system suitable for use in a chair.

FIG. 6 shows a top view of a pentagonal wall frame suitable for use as a floor, buttressed with a compact series of triangular supports each of the present invention.

FIG. 7 shows a pyramid-like structure suitable for use as a building of three or more stories, requiring only three or four lengths of struts.

FIG. 8 shows the axes and nuclei of all of the front-most nodes of the structure of FIG. 7.

FIG. 9 shows a spaceframe structure of the present invention that would be suitable for a swimming pool.

FIG. 10 shows the axes and nuclei that correspond with struts and nodes of the rear right quarter of FIG. 9.

FIG. 11 shows an architectural system useful for constructing a lightweight, very rigid tower.

FIG. 12 shows a node and strut configuration suitable for use with some embodiments of the present invention at a 1:1 scale.

FIG. 13 shows a magnified cross section of the bolt and node of FIG. 12, fully engaged with one another.

FIG. 14 shows three nodes each formed by a different type of slice across a node like that of FIG. 12.

FIG. 15 shows a more complex and versatile polyhedral node which can be used for any of the nodes of any of the structures shown in FIGS. 3-11.

FIG. 16 shows another modular “shell-type” node suitable for use as any of several of the nodes in structures shown in FIGS. 7 & 11.

FIG. 17 shows several straps like those of FIG. 16, drawn to scale in various positions.

FIG. 18 shows the construction of another style of composite node.

FIG. 19 shows how a gap between two of the components of the composite node of FIG. 18 permit a tongue of a strut to be inserted therebetween.

DETAILED DESCRIPTION

Although the examples below show more than enough detail to allow those skilled in the art to practice the present invention, subject matter regarded as the invention is broader than any single example below. The scope of the present invention is distinctly defined, however, in the claims at the end of this document.

Numerous aspects of spaceframe architecture that are not a part of the present invention (or are well known in the art) are omitted for brevity, avoiding needless distractions from the essence of the present invention. For example, this document does not include much detail about material selection or node design, except where the inventor has observed opportunities for a synergy.

Definitions and clarifications of certain terms are provided in conjunction with the descriptions below, all consistent with common usage in the art but some described with greater specificity. As used herein, an “axis” of a strut refers to a line segment very closely aligned with the strut. An axis has a “length,” ordinarily greater than that of the corresponding strut, bounded by nuclei of two nodes with which the strut engages. As used herein, a “nucleus” of a node is a point (usually within the node) aligned with the axes of struts that engage with the node. For nodes that are not substantially round, a nucleus will be approximately equidistant from two or more node surfaces that each engage a strut. As used herein, a “radius” of a node refers to a distance measured from a nucleus to a farthest surface from the nucleus. Thus, the term is defined even for nodes of irregular shape. Two angles are “substantially equal” herein if they are within half a degree. Other quantities are “substantially equal” if they are within 0.5% of each other.

A “complete” strut is one that substantially surrounds its corresponding axis for the entire length between the nodes engaged by the strut. Such a strut will distribute an axial tension or compression on opposing sides of the axis. An arcuate or other “incomplete” strut, by contrast, will bow further away from the axis under axial compression. This greatly reduces the rigidity of the system, or necessitates a needless increase in strut weight.

Turning now to FIG. 1, there is shown a basic architectural system 100 of the present invention. A triangular base 101 comprises three nodes 110, 130, 150 and three complete struts 120, 140, 160. Strut 120 engages nodes 110, 130 and is substantially aligned along axis 129. Strut 140 engages nodes 130, 150 and is substantially aligned along axis 149. Strut 160 engages nodes 110, 150 and is substantially aligned along axis 169. Base plane 199 contains the three axes 129, 149, 169 and their endpoints 119, 139, 159. An extension 102 comprises at least one complete strut 170 extending from the triangular base non-orthogonally (i.e. substantially aligned along an axis 179 forming a substantially acute angle 198 with base plane 199).

FIG. 2 is a chart summarizing which figures in this description illustrate which integer values as used in the formulas described in the summary above. Column 288, for example, indicates that a triangular base of FIG. 5 corresponds with j=r=2 and n=1. Using the formula, one expects a first interior angle of 79.2 degrees, which is in fact formed between the axes of struts 525, 527. One similarly expects a second interior angle of 63.4 degrees, which is formed between the axes of struts 527, 528. The third interior angle is less than 60 degrees, also. One of ordinary skill will readily be able to apply the formula and identify the triangular base(s) corresponding to any of the columns in FIG. 2, as it is shown in subsequent figures. FIG. 2 illustrates that a wide variety of triangular bases suitable for use in the present invention are illustrated in these figures.

FIG. 3 shows a simple, trilaterally symmetric architectural system 300 of the present invention, suitable for use in a table. Three inner nodes 310 and six outer nodes 320, 330 are positioned at the surface of the table. Identical tabletop struts 311, 321, 331 couple each inner node 310 to two outer nodes 320, 330 in an equilateral triangle. The equilateral triangles are coupled to one another by longer struts 312, 313 as shown. The nodes 310, 320, 330 of each equilateral triangle are each coupled to a knee-height node 340 by a respective upper support strut 314, 324, 334. Floor nodes 350 are each coupled to a respective inner node 310 by a vertical strut 315. Floor nodes 350 are also each coupled to a respective knee-height node 340 by a lower support strut 317. The 37.4° angle indicated in the left-most data column of FIG. 2 is between axes 459, 479. The 101° angle between axes 449, 479 corresponds with r=2 and t=1. The extension comprises, for example, the strut substantially aligned with axis 448. FIGS. 3 & 4 thus embody the present invention, as do FIGS. 6-11.

FIG. 4 shows an enlarged view 400 of the respective positions of the nuclei 410, 420, 430, 440 of some of the nodes 310, 320, 330, 340 of FIG. 3. Each dotted line represents an axis along which a respective strut is aligned. For example, each lower support strut is aligned along a respective axis 379. Each vertical strut 315 is aligned along a respective axis 459. Each inner node support strut 314 is aligned along a respective axis 449. Axes 449, 459, 479 form a triangle defining the (vertical) base plane. Axes 449, 459 form an interior angle of the base triangle about equal to 2×20.9° (j=2,k=m=n=0). Axes 449, 479 form an interior angle about equal to 2×31.7°+37.4° (r=2,t=1,q=s=0). The third interior angle is less than 60°. Outer node support struts 334 are each aligned along a respective axis 448 that forms a substantially acute angle with the base plane.

It will be appreciated by those skilled in the art that the structure of FIGS. 3 & 4 provides a higher degree of rigidity than comparable structures of the prior art, for a given choice of material. Moreover, the structure is built with only six lengths of struts.

FIG. 5 shows a simple, bilaterally symmetric architectural system 500 suitable for use in a chair. Nodes 510, 520 are at two comers of a square formed by struts 501, 511, 521, 531. Nodes 520, 530 are likewise at two comers of a rectangular seat frame formed by struts 514, 524, 531, 541. The seat side struts 514,524 are shorter than the back side struts 511,521 so that node 520 is offset from node 530 by about 13.4% less than it is offset from node 510.

Struts 524 and 528 are aligned along respective axes that form a 37.4° angle. Struts 524 and 561 are aligned along respective axes that form an angle about equal to 20.9°+20.9°+31.7°+37.4°. Thus it would appear that struts 524, 528, 561 (with nodes 520, 530, 540) would form a suitable base triangle of the present invention, in a vertical plane. Unfortunately, this design has a noteworthy weakness: All of the direct extensions from this base triangle extend either along within the same plane (i.e. struts 525, 527 to node 550) or perpendicular to the plane (i.e. “aligned substantially parallel to” strut 531). Applicant has determined that such designs are often not adequately rigid to resist a shear force parallel to the base plane. Such designs can therefore be susceptible to vibration, deformation and degradation that can have severe consequences in larger scale applications.

FIG. 6 shows a top view of a pentagonal wall frame 600 suitable for use as a floor, buttressed with a compact series of triangular supports each of the present invention. The frame 600 includes five outer nodes 610, 640 and five inner nodes 630, 660 that all lie in a primary plane. Five intermediate nodes 620, 650 all lie in a secondary plane (behind the primary plane, as shown).

Struts 612, 614, 624 are substantially aligned along respective axes that form an isosceles triangle with two interior angles of about 20.9° and one of about 140.2°. (Note that this is equal to 31.7°+31.7°+37.4°+37.4°.) A triangular base of the same size and shape is formed by strut 624 with struts 622, 634.

Struts 631, 632, 642 are substantially aligned along respective axes that form an isosceles triangle with two interior angles of about 72° and one of about 36°. (Note that this corresponds to a triangle with m=s=2 and j=k=n=q=r=t=0, in terms to the formula given in the summary.) A larger base triangle forming these same angle is formed with corners in nodes 610, 640, 670. Note that the longer sides of this base triangle are very long in comparison to their thickness. Rigidity is maintained, however, because each is a “supported strut,” one that includes a radially protruding extension (such as strut 631) generally supporting the mid-section of the supported strut. Finally, another advantage of frame 600 is the small variety of struts required to build it. As shown, only four lengths of (unsupported) struts are used.

FIG. 7 shows a pyramid-like structure 700 suitable for use as a building of three or more stories. (For clarity, nodes and struts in FIG. 7 are shown with a larger-than-typical diameter, relative to their lengths.) As shown, structure 700 can be built with only three lengths of struts.

Three of the nodes of pentagonal wall frame 600 are re-used in FIG. 7. This illustrates that frame 600 can be used as an especially rigid and compact floor in structure 700. In this case, the intermediate nodes 620, 650 form a horizontal pentagon of the same size and orientation as that of node 780. Also, building structure 700 to incorporate frame 600 requires a total of only four lengths of struts.

FIG. 8 shows the axes and nuclei of all of the front-most nodes of structure 700. Interior and posterior nodes and struts (shown in FIG. 7) are omitted for simplicity and to resemble how structure 700 would appear when covered by conventional walls. Nuclei 810, 840, 870, 880 correspond respectively to nodes 610, 640, 670, 780 of FIG. 7.

FIG. 9 shows a spaceframe structure 900 of the present invention that would be suitable for a swimming pool. The rear half 901 is symmetric with the front half, and the right half 902 is symmetrical with the left. Only five lengths of struts are required for constructing this spaceframe, as shall be illustrated with respect to FIG. 10.

FIG. 10 shows the axes and nuclei that correspond with struts and nodes of the rear right quarter of FIG. 9. The axes 1017, 1027, 1037, 1047, 1057, 1067, 1077 are all of the same length L. These axes are respectively aligned with seven of the 20 shortest struts shown in FIG. 9. These 20 struts have substantially the same length (i.e. to within typical manufacturing tolerances) as one another. The 20 struts are shorter than L so as to allow each node to which the strut affixes to occupy the respective nucleus.

Axes 1031, 1041, 1051, 1061, 1071, 1081 are each longer than L by about 5.14%. Each is substantially aligned with a strut about as long as L shown in structure 900, of which there are 16. Similarly there are five struts in structure 900 having a maximum length, each aligned along a respective axis such as axes 1042, 1052, 1082. Structure 900 also contains 16 basically identical struts somewhat shorter than those of maximum length, aligned along axes like 1018, 1048, 1058, 1078, 1088. And finally, structure 900 contains eight basically identical, medium-length struts aligned along axes like 1045, 1085.

Struts or axes having the same last digit, within FIG. 10, have substantially the same length as one another. The same holds true within any given one figure elsewhere in this document. In fact, the relative proportions between axis lengths can be derived from the angles given, in a triangle, or vice versa. Moreover the axis lengths are to scale (typically oblique) for all of the figures in this document. For these reasons it suffices to give angles or lengths to enable the construction of further frames shown in this document.

FIG. 11 shows an architectural system 1100 useful for constructing a lightweight, very rigid tower. Nucleus 1110 is the highest point, stellated from a pentagonal base comprising nuclei 1120, 1130, 1140, 1150. FIG. 11 shows all of the angles of the surface of the “wedge” bounded by nuclei 1110, 1130, 1140, 1170, 1180 are shown explicitly. This wedge is used a total of five times about the highest nucleus 1110.

The base of the system 1100 is a pentagon having five sides (including axis 1112) and five points (including nuclei 1170, 1180). A base triangle of the present invention includes axes 1112, 1117, 1127 and nuclei 1170, 1180 and angles as shown within that triangle.

One surface axis, the one just below axis 1137, is not shown so as to reveal the position of a horizontal axis 1132 the same length as that of base axis 1112. This horizontal axis 1132 is part of two base triangles of the present invention, with angles as shown. The complete structure includes a total of twenty horizontal axes like 1112, 1132. Twenty substantially identical struts (not shown) aligned along these axes provide four pentagonal floors within structure 1100. If desired, each of these simple floors can be augmented by using a vertically compact pentagonal frame like frame 600 of FIG. 6.

FIG. 12 shows a node 1210 and strut 1290 configuration suitable for use with some embodiments of the present invention at a 1:1 scale. Strut 1290 comprises a solid rectangular plank of a hardwood 1289, a steel strap, and a threaded bolt 1299. The steel strap comprises a left portion 1291, a right portion 1292, and an engagement portion 1293.

Node 1210 is an aluminum polyhedron having a threaded hole 1211 in each exterior side. When bolt 1299 engages node 1210 as indicated, the angled portions of the sides 1291, 1292 yield slightly to permit a solid engagement between the engagement portion 1293 of the strap and the top surface of the node 1210 even if the strut 1290 is slightly too long or short. Even while providing this flexibility, strap is wide, thick, and short enough as shown to make the overall node/strut joint highly rigid so long as the disengaged strap position (i.e., the position along axis 1297 at which the strut has axial stresses of 1 Newton or less) is within about R/50 of node 1210, where R is the radius 1298 of node 1210.

The closest successive holes 1211 of node 1210 are 36 degrees apart (although some sides 1212 lack engagement holes so as to simplify node manufacture). Node 1210 is therefore also capable of supporting rigid angles of 72 degrees and 108 degrees, the same ones required for structure 700 (of FIG. 7). A problem may exist, however, that would require a modification of the node 1210 or strut 1290 to enable the construction of structure 700. FIG. 12 shows a node radius 1298 that is less than half of the maximum strut diameter 1288. For this reason, it may be impossible to have several struts engage with node 1210 simultaneously in a desired configuration. For example, it may be desirable to replace node 1298 with one having a radius that is 50% larger than that shown (but without enlarging the engagement holes 1211).

FIG. 13 shows a magnified cross section of bolt 1299 fully engaged with node 1210, holding engagement portion 1293 solidly against an outer surface of node 1210. A preferred mechanism for doing this is the use of a strut having several load surfaces 1215, 1216 protruding (radially) from the axis 1297. The load surfaces 1215, 1216 are configured to permit axial force transfer from access surfaces 1295, 1296 of the strut 1290. A threaded configuration like this can easily be made to resist relative movement between the node 1210 and strut 1290 under axial compression or tension in excess of 100 Newtons or more.

More sophisticated engagement mechanisms are available. For example, U.S. Pat. No. 4,193,706 (“Bolt Connections Between Tubular Rods and Junctions in Three-Dimensional Frameworks”) issued 18 Mar. 1980 to Eberlein et al. teaches one such system. Similar systems are available for purchase from Mero Structures, Inc. in Menomonee Falls, Wis. (262-255-5561,www.mero.com).

FIG. 14 shows three nodes 1410, 1420, 1430 each formed by a different type of slice across a node like 1210 (of FIG. 12). These would be suitable for use in some of the positions of structure 700 (of FIG. 7). When used as outer corner nodes, a flat side of one of these could be used so that the node would protrude less from the structure. This would also reduce the weight of the structure with a fairly small loss of rigidity.

FIG. 15 shows a more complex and versatile polyhedral node 1510 which can be used for any of the nodes of any of the structures shown in FIGS. 3-11. A half of this node 1520 is also shown, revealing its inner structure. Note that the interior 1525 is formed merely by boring a hole into the center of each side, the result being a large, multi-lobed cavity that compromises very little of the rigidity of the original solid polyhedron.

FIG. 16 shows a “shell-type” node 1600 suitable for use as any of several of the nodes in structures shown in FIGS. 7 & 11. Several straps 1610 make up the shell, preferably made of steel. The ends of five straps converge to form a roughly circular hole 1611 which can be used for securing a strut. The strut can be a bolt and nut configured to secure the five straps 1610, but more preferably the straps are welded or adhesed to one another and to the strut. In the mid-section of each strap 1610 is a slot 1612. The slot of each strap provides a very broad range of angular positions any of which can be used to secure a cylindrical strut by conventional means. For the entire structure of FIG. 11, all of the necessary angles can be achieved with struts positioned at end-holes (like 1611) and at the center of slots (like 1612). Because FIG. 16 is shown to scale, one of ordinary skill can easily determine what other angles between axes of struts are enabled using nodes of this design. FIG. 17 shows several straps 1721, 1722, 1723, 1724 identical to 1610 to scale, defining the components of node 1600 with greater clarity.

FIG. 18 shows the construction of another style of composite node 1800. FIG. 19 shows how a gap between two of the components 1911, 1912 of the composite node 1800 permit a tongue 1993 of a strut 1990 to be inserted therebetween. Inter-strut angles as small as 36° are achievable with nodes identical to 1800, which is all that is needed for a structure like that of FIG. 7. During assembly, a bolt or other fastening mechanism squeezes the components 1912 together, completing the node and securing the tongue against axial (vertical) displacement relative to node 1800. Once the tongue is moved into position, conventional wood screws (not shown) affix the Y-shaped member comprising the tongue 1993 to the rest of the strut 1989.

Alternatively characterized, a first embodiment of the present invention includes a triangular base (such as 101) which engages an extension (such as 102). The base includes three complete struts substantially aligned along their respective axes. These axes each intersect each other to form a triangle contained in a base plane. The triangle's vertices each correspond to a respective nucleus of nodes called A, B and C. This forms three base angles (called CAB, ABC, and CBA). Angle CAB has a positive value about equal to [j×20.9°+k×31.7°+m×36°+n×37.4°], where j, k, m and n are each an integer less than three. Angle ABC also has a positive value about equal to [q×20.9°+r×31.7°+s×36°+t×37.4°],where q, r, s and t are each an integer less than three. Note that these angular constraints can impose size limitations on the nodes. For example, the third node (C) engages the second and third complete struts and must be large enough to maintain the third base angle BCA at a positive value less than 60°. Note also that these angular restraints permit a great variety of combinations. For example, j, n, q and t may all be even in a given base triangle.

At least one of the base triangle struts comprises two or more rigid pieces (such as 1289, 1299) able to move apart so as to produce a strut elongation. The extension comprises a fourth complete strut substantially aligned along a fourth axis forming a substantially acute angle with the base plane.

In a second embodiment, the fourth axis forms an angle with the first, second or third axis that is substantially equal to a reference angle. The reference angle is selected from a group consisting of 13.3°, 15.5°, 20.9°, 22.2°, 31.7°, 35.3°, 36°, 37.4°, 37.8°, 41.8°, 44.5°, 45°, 54.7°, 58.36°, 60°, 63.4°, 65.9°, 69.1°, 70.5°, 72°, 75.5°, 76.7°, 79.2°, 82.2°, 90°, 97.8°, 100.8°, 103.3°, 104.5°, 108°, 109.5°, 110.9°, 114.1°, 116.6°, 120°, 121.7°, 125.3°, 135°, 135.5°, 138.2°, 142.2°, 142.6°, 144°, 144.7°, 148.3°, 155.9°, 157.8°, 159.1°, 164.5°, and 166.7°. The extension (such as 102) comprises a polygon (such as a triangle or quadrilateral, see FIG. 9) having N sides each occupied by a respective complete strut. The third axis contains one of the N sides, and the fourth axis contains another of the N sides.

In a third embodiment, one of the struts (such as 170) has a maximum diameter D (such as 1288) and one of the nodes (such as 110) has a radius R (such as 1298) that is not less than D/2. The struts are each primarily composed of a non-metallic material (such as wood). Each of the base's nodes includes couplings engaging two of the struts of the base triangle. Each of the couplings is capable of retaining its strut in a fixed position relative to the node, even under a tension of at least 100 Newtons along the axis therebetween. This is optionally accomplished by providing load surfaces (such as 1215, 1216) on each node and access surfaces (such as 1295, 1296) on each strut. (These access surfaces are those configured to exert force each on a respective one of the load surfaces so as to resist an axial movement of the strut relative to the node.)

All of the structures and methods described above will be understood to one of ordinary skill in the art, and would enable the practice of the present invention without undue experimentation. It is to be understood that even though numerous characteristics and advantages of various embodiments of the present invention have been set forth in the foregoing description, together with details of the structure and function of various embodiments of the invention, this disclosure is illustrative only. Changes may be made in the details, especially in matters of structure and arrangement of parts within the principles of the present invention to the full extent indicated by the broad general meaning of the terms in which the appended claims are expressed. Although the preferred embodiments described herein are largely directed to conventional fasteners for node/strut couplings, it will be appreciated by those skilled in the art that many teachings of the present invention can be applied to other types of couplings without departing from the scope and spirit of the present invention. 

1. An architectural system comprising: a triangular base comprising: first, second and third complete struts substantially aligned along first, second and third axes (AB, BC, and AC) respectively, the axes all contained within a base plane, the first and third axes forming a first base angle CAB, the first and second axes forming a second base angle ABC, the second and third axes forming a third acute base angle BCA, more than one of the struts each comprising at least two rigid pieces able to move apart so as to produce a strut elongation; a first node A engaging the first and third complete struts, the first node A large enough to maintain the first base angle CAB, the first base angle CAB consisting of a first positive value about equal to (j×20.9°+k×31.7°+m×36°+n×37.4°), where j, k, m and n are each an integer less than three; a second node B engaging the first and second complete struts, the second node B large enough to maintain the second base angle ABC, the second base angle ABC consisting of a second positive value about equal to (q×20.9°+r×31.7°+s×36°+t×37.4°) , where q, r, s, and t are each an integer less than three; a third node C engaging the second and third complete struts, the third node C large enough to maintain the third base angle BCA at a third positive value less than 60°, and wherein the integers j, k, m, n, q, r, s, and t are constrained such that the first, second, and third base angles add to 180°; and an extension engaging the triangular base and comprising a fourth complete strut substantially aligned along a fourth axis that forms a substantially acute angle >3° with the base plane.
 2. The architectural system of claim 1 in which the fourth axis forms an angle DAB with the first axis that is substantially equal to a reference angle selected from a group consisting of 13.3°, 15.5°, 20.9°, 22.2°, 31.7°, 35.3°, 36°, 37.4°, 37.8°, 41.8°, 44.5°, 45°, 54.7°, 58.3°, 60°, 63.4°, 65.9°, 69.1°, 70.5°, 72°, 75.5°, 76.7°, 79.2°, 82.2°, 90°, 97.8°, 100.8°, 103.3°, 104.5°, 108°, 109.5°, 110.9°, 114.1°, 116.6°, 120°, 121.7°, 125.3°, 135°, 135.5°, 138.2°, 142.2°, 142.6°, 144°, 144.7°, 148.3°, 155.9°, 157.8°, 159.1°, 164.5°, and 166.7°.
 3. The architectural system of claim 1 in which the fourth axis forms an angle with the second axis that is substantially equal to a reference angle selected from a group consisting of 13.3°, 15.5°, 20.9°, 22.2°, 31.7°, 35.3°, 36°, 37.4°, 37.8°, 41.8°, 44.5°, 45°, 54.7°, 58.3°, 60°, 63.4°, 65.9°, 69.1°, 70.5°, 72°, 75.5°, 76.7°, 79.2°, 82.2°, 90°, 97.8°, 100.8°, 103.3°, 104.5°, 108°, 109.5°, 110.9°, 114.1°, 116.6°, 120°, 121.7°, 125.3°, 135°, 135.5°, 138.2°, 142.2°, 142.6°, 144°, 144.7°, 148.3°, 155.9°, 157.8°, 159.1°, 164.5°, and 166.7°.
 4. The architectural system of claim 1 in which the fourth axis forms a fourth angle with another of the axes that is substantially equal to a reference angle selected from a group consisting of 13.3°, 15.5°, 20.9°, 22.2°, 31.7°, 35.3°, 36°, 37.4°, 37.8°, 41.8°, 44.5°, 45°, 54.7°, 58.3°, 60°, 63.4°, 65.9°, 69.1°, 70.5°, 72°, 75.5°, 76.7°, 79.2°, 82.2°, 90°, 97.8°, 100.8°, 103.3°, 104.5°, 108°, 109.5°, 110.9°, 114.1°, 116.6°, 120°, 121.7°, 125.3°, 135°, 135.5°, 138.2°, 142.2°, 142.6°, 144°, 144.7°, 148.3°, 155.9°, 157.8°, 159.1°, 164.5°, and 166.7°.
 5. The architectural system of claim 4 in which one of the struts has a maximum diameter D and in which one of the nodes has a radius R that is not less than D/2.
 6. The architectural system of claim 4 further comprising a polygon structure coupled to the fourth complete strut, the polygon structure having N sides each occupied by a respective complete strut, the third axis containing one of the N sides, the fourth axis containing another of the N sides wherein the fourth complete strut forms a portion of the polygon structure.
 7. The architectural system of claim 4 in which j=0.
 8. The architectural system of claim 4 in which j and q are both even.
 9. The architectural system of claim 4 in which j=1.
 10. The architectural system of claim 4 in which n and t are both even.
 11. The architectural system of claim 4 in which each of the nodes has a radius R and in which each of the struts has a respective diameter less than 2R.
 12. The architectural system of claim 4 in which the second node includes first and second couplings respectively engaging the first and second complete struts, the first coupling capable of retaining the first strut under a tension of 100 Newtons along the first axis (AB), the second coupling capable of retaining the second strut under a tension of 100 Newtons along the second axis (BC).
 13. The architectural system of claim 4 in which the struts are primarily composed of a non-metallic material.
 14. The architectural system of claim 4 in which m=0.
 15. The architectural system of claim 1 in which m=0.
 16. The architectural system of claim 1 in which j≠q.
 17. The architectural system of claim 1 in which q<2.
 18. The architectural system of claim 1 in which k=0.
 19. The architectural system of claim 1 in which k and r are both even.
 20. The architectural system of claim 1 in which k≠1.
 21. The architectural system of claim 1 in which n=t.
 22. The architectural system of claim 1 in which j=0.
 23. The architectural system of claim 1 in which j and q are both even.
 24. The architectural system of claim 1 in which j=1. 